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For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of −5 and −2 as well.
If n is a power of an odd prime number the formula for the totient says its totient can be a power of two only if n is a first power and n − 1 is a power of 2. The primes that are one more than a power of 2 are called Fermat primes , and only five are known: 3, 5, 17, 257, and 65537.
The general formula is X k + 1 = a ⋅ X k mod m , {\displaystyle X_{k+1}=a\cdot X_{k}{\bmod {m}},} where the modulus m is a prime number or a power of a prime number , the multiplier a is an element of high multiplicative order modulo m (e.g., a primitive root modulo n ), and the seed X 0 is coprime to m .
lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization.
The exponent of the group, that is, the least common multiple of the orders in the cyclic groups, is given by the Carmichael function (sequence A002322 in the OEIS). In other words, λ ( n ) {\displaystyle \lambda (n)} is the smallest number such that for each a coprime to n , a λ ( n ) ≡ 1 ( mod n ) {\displaystyle a^{\lambda (n)}\equiv 1 ...
A 24×60 rectangular area can be divided into a grid of 12×12 squares, with two squares along one edge (24/12 = 2) and five squares along the other (60/12 = 5). The greatest common divisor of two numbers a and b is the product of the prime factors shared by the two numbers, where each prime factor can be repeated as many times as it divides ...
Multiply-with-carry PRNGs with a multiplier of a are equivalent to LCGs with a large prime modulus of ab r −1 and a power-of-2 multiplier b. A permuted congruential generator begins with a power-of-2-modulus LCG and applies an output transformation to eliminate the short period problem in the low-order bits.
LCM may refer to: Computing and mathematics. Latent class model, a concept in statistics; Least common multiple, a function of two integers; Living Computer Museum;